In the end, it is enough to ask whether or not the total partition function that contains all the twisted sectors vanish.
We will clarify the `criterion' to this aim, and present a classification of the relevant orbifold models leading to
the string vacua with the desired properties.
In some cases, the desired vacua can be constructed in the manner similar to those given in
[1]} for the type II string, in which the orbifold groups contain two generators equipped with some discrete torsions
[2]}, [3]}, [4]}.
On the other hand, we also find out the simpler models which are just realized
as the asymmetric orbifolds of cyclic groups with only one generator, in contrast to the type II string cases.
